Pith Number

pith:HCG6RWYZ

pith:2026:HCG6RWYZJV423FOF3LOGMJTYUB

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A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 $\&$ -2 isomorphic circulant graphs

Vilfred Kamalappan, Wilson Peraprakash

Computer programs generate families of Type-2 isomorphic circulant graphs for m values 2, 3, 5, 7 and odd primes p.

arxiv:2605.14140 v1 · 2026-05-13 · math.CO

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\pithnumber{HCG6RWYZJV423FOF3LOGMJTYUB}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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Claims

C1strongest claim

Using a C++ computer program, the authors obtained families of Type-2 isomorphic C_n(R) w.r.t. m = 2,3,5,7 for n in natural numbers as well as C_{np^3}(R) w.r.t. m = p for odd prime p.

C2weakest assumption

The programs correctly implement the definitions of Type-1 and Type-2 isomorphism from the cited prior papers without coding errors or missed cases.

C3one line summary

Computer programs are supplied to generate families of Type-2 isomorphic circulant graphs C_n(R) for m=2,3,5,7 and to demonstrate how Type-1 and Type-2 isomorphisms occur.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] A. Adam,Research problem 2-10, J. Combinatorial Theory,3(1967), 393 1967

[2] Bjarne Stroustrup,The C++ Programming Language, Addison-Wesley, 2013 2013

[3] B. Elspas and J. Turner,Graphs with circulant adjacency matrices, J. Combinatorial Theory,9(1970), 297-307 1970

[4] Fisher Larence,Visual Basic.NET: An Introduction to Computer Programming, Kendall Hunt Publishing, USA 2015

[5] Martin Grohe and Pascal Schweitzer,The graph isomorphism problem, Communication ACM,63 (11)(2020), 128– 2020

Receipt and verification

First computed	2026-05-17T23:39:11.697517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

388de8db194d79ad95c5dadc662678a06ba270b61b71166618d6be5415f2badc

Aliases

arxiv: 2605.14140 · arxiv_version: 2605.14140v1 · doi: 10.48550/arxiv.2605.14140 · pith_short_12: HCG6RWYZJV42 · pith_short_16: HCG6RWYZJV423FOF · pith_short_8: HCG6RWYZ

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Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HCG6RWYZJV423FOF3LOGMJTYUB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 388de8db194d79ad95c5dadc662678a06ba270b61b71166618d6be5415f2badc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a24eba99ae13e454d966dcf22697201e2644886d98df17f3006cd9979efd6152",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T21:46:47Z",
    "title_canon_sha256": "6aa26622ab3e18b30aef5e43a430fce4e78a5e1ea948122020b557fc6fe79169"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14140",
    "kind": "arxiv",
    "version": 1
  }
}